BMAD Posted May 10, 2013 Report Share Posted May 10, 2013 What's the maximum product of any whole number of real numbers whose sum is 100? What are they? Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted May 10, 2013 Report Share Posted May 10, 2013 What's the maximum product of any whole number of real numbers whose sum is 100? What are they? They should be the same numbers, so 100/n is the form and (100/n)^{n} is the solution. I get n = 37 Product = 9 474 061 716 781 820 Interestingly, n = 25 and n = 50 give the same product, namely 1 125 899 906 842 624. If n need not be integral, n =100/e gives 9 479 842 689 868 740 Quote Link to comment Share on other sites More sharing options...

0 James33 Posted May 10, 2013 Report Share Posted May 10, 2013 Is it infinity? If I take the 3 numbers 2a+100, -a, -a then the sum is 100 but the product is (2a+100)a^2 which is unbounded as a->infinity. Quote Link to comment Share on other sites More sharing options...

0 dark_magician_92 Posted May 10, 2013 Report Share Posted May 10, 2013 36 times e i.e. e^36, multiplied by e^(100-36*e) The product would be = e^100/e Quote Link to comment Share on other sites More sharing options...

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What's the maximum product of any whole number of real numbers whose sum is 100? What are they?

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